On your laptop, when you're noticing slow downs, if you check the task manager, do you see your processor utilization very high, or maybe the memory utilization very high or maybe even both? Or is the slower harddrive in the laptop the problem (average laptop drive runs 5400 rpm where desktop drives spin at 7200 rpm)?

Did you want another laptop or were you wanting to go for a Desktop for this?

If a desktop is fine, then pretty much any system with a dual core processor (even if it's an AMD 3800 dual core or Intel E2140) and 2 GB of memory should easily be able to make your webdesigning a lot smoother experience. I would however recommend to get a (mini) tower and not a slim tower, as it would allow upgrading (in the future) to a regular videocard. For webdesign this isn't very important, so using onboard (initially) will work fine, but if you ever want to extend the life of your system (a year or 2 down the road), the ability to put in a full height PCIe videocard would be nice.

If you're wanting to get another laptop, you first have to decide which size; 12", 13", 15", or 17". Then decide if you want to go with the integrated video option, or a 'real' videocard as chosing the integrated option on a laptop usually means there's no upgrade path. I'd go with 2GB of memory or more and consider getting a 7200 rpm laptop drive (more expensive, but may be worth it for your tasks).